Referring to Sampling, filters, windowing, FFT. From theory to help on this coding list with the figure, I now have some more questions.
How will taking every third of the 48 kHz vs. taking the mean of three relate to the first anti-aliasing filter F1?
I assume that in both cases I would need filter F2?
It's not quite clear what you are trying to do here.
If you just want to down-sample from 48kHz to 16kHz you should apply a "good" low pass filter, F1, and then simply throw away every 2nd and 4rd sample.
"Good" here is defined by the requirements of your application. It's a tricky tradeoff between residual aliasing, the amount of usable bandwidth, and artifacts in the time and frequency domain. Chances are a single biquad will NOT work here.
How will taking every third of the 48 kHz vs. taking the mean of three relate to the first anti-aliasing filter F1?
Taking the mean of three is a moving average filter with a transfer function of $H(z) = \frac{1}{3}[1+z^{-1} + z^{-2}]$. This is half low pass half comb filter and a very poor choice for an anti-aliasing filter.
I assume that in both cases I would need filter F2?
I don't understand what your filter F2 is supposed to be doing. What it is for ?
